Chronoamperometry

Chronoamperometry • Stationary electrode • Unstirred = mass transport by diffusion • Constant potential • Measure current vs time Theory assume Ox + n e- Red - both Ox and Red are soluble - reversible reaction (electrochemically) - potential set so reduction goes to completion at the electrode surface Components of output signal in Chronoamperometry

IFar decreases because Ox used up at electrode surface and Ox is only replenished by diffusion

Faradaic current (IFar) follows Cottrell equation I Capacitive current (Icap) (current) decays exponentially for a constant applied potential

t (time)

Icap is high as electrode capacitive layer charges up, then drops off Processes perturbing system can cause data to differ from Cottrell Equation 1) Capacitive Current – charging current is exponential as shown -kt Icap = e Note: Capacitive current decreases more rapidly than Faradaic current so at longer times the ratio IFar/Icap is larger 2) Occurrence of coupled chemical reactions e.g. Ox + n e- Red 2 Red A A + n e- B Affects the shape of the current-time curve Chronoamperometry Applications • Can measure concentration by measuring I vs conc. at any fixed time • Can analyze the shape of the current-time curve in order to study coupled chemical reactions • There are better ways to do both of these with more modern techniques • Chronoamperometry is important because it is a fundamental method on which other techniques are based Chronopotentiometry • Stationary electrode • Unstirred = mass transport by diffusion • Constant current applied between electrodes • Measure potential vs time Theory Galvanostat assume Ox + n e- Red - both Ox and Red are soluble - reversible reaction (electrochemically) - apply current and use up Ox at electrode surface producing Red [Ox]

Ox + n e- Red

Apply current & use up Ox at electrode surface while producing Red

[Red] Theory of Chronopotentiometry

0.059 [Red] E = Eo ------log ------n[Ox]

A gradual change in E occurs as [Red] goes up and [Ox] goes down (transition region) Ultimately the surface concentration of Ox goes to zero & to sustain the constant current applied, electrode potential makes a rapid change to the value required to make a new process go Chronopotentiometry Output Wave

Transition Time (τ)

Point at which Ox E is used up

At start no Red is present so E is not defined

time

½Q)$'½& 2[ 6DQG(TXDWLRQ ½ τ L Summary of Chronopotentiometry • In principle quantitative analysis can be ½ done by relating τ WR&R[ • ,QUHDOLW\LWLVEHWWHUGRQHE\RWKHUPHWKRGV • &KURQRSRWHQWLRPHWU\ LOOXVWUDWHVFRQVWDQW FXUUHQWVLWXDWLRQLQHOHFWURFKHPLVWU\ • &KURQRSRWHQWLRPHWU\ LVYHU\SRRUDW KDQGOLQJFDSDFLWLYHFXUUHQW Coulometry Methods based on counting coulombs (C), the basic unit of electrical charge (Q)

Q M Faraday’s Law W = ------n F

Where: M = molecular weight (g/mole) W = weight (g) n = number of electrons (unitless) F = Faraday’s constant (96,500 C/mol) Fundamental assumption is that reaction is 100 % current efficient i.e, all coulombs go to oxidizing or reducing species of interest

Kinds of coulometry 1) Controlled Potential Coulometry t Nothing more than integrating area under the curve in chronoamperometry Q = i dt 0 Can be referred to as chronocoulometry 2) Constant Current Coulometry

Care must be taken so that there is enough Q = i t stuff to carry the current at electrode surface Rarely used anymore Major application is coulometric titrations where titrant is prepared electrochemically and standardized by counting coulombs e.g. bromine Br2 as titrant - - 2 Br Br2 + 2 e 1) Useful for titrants that can’t be stored as stable solutions 2) Small currents can be measured accurately so even very dilute titrants can be used 3) In theory can count coulombs for any method where current is measured by integrating Coulometric cell

- - 2 Br Br2 + 2 e

Br2 + C6H10 C6H10Br2

Voltammetry (stirred) • Stationary electrode • Stirred = mass transport by convection • Vary potential linearly with time • Measure current vs time Theory assume Ox + n e- Red - both Ox and Red are soluble - reversible reaction (electrochemically) - potential varies Define - Limiting Current as steady state current when [Ox] = 0 at electrode surface i.e., applied potential is sufficiently cathodic such that all Ox is reduced at electrode

nFADC I = ------bulk transport-limited current δ I limiting current

Gives quantitative E information

Nernst controlled current RT [Red] E = Eo ------ln ------nF [Ox] quantitative information

qualitative information

for stirred solution Linear Scan Voltammetry (stirred)

Ox + e- Red

IC = Capacitive current IL = Limiting current I E½ = Half wave potential L I

E E ½ Linear Scan Voltammetry (stirred)

Ox + e- Red

Half wave potential (E½)

is E when I = IL/2 IL I

E E ½ Linear Scan Voltammetry (stirred)

Ox + e- Red

I is proportional to [Red],

IL represents the situation where Red is maximum IL I and Ox is zero.

E E ½ Linear Scan Voltammetry (stirred)

Ox + e- Red

When I = IL/2, then [Red] = [Ox] and I E = E L I ½ RT (IL –I) E = E½ ------ln ------nF I

E E ½ Linear Scan Voltammetry (stirred)

reversible irreversible more irreversible I

most irreversible

E Can assign rate constants (k) for irreversible processes Linear Scan Voltammetry (stirred)

For two reversible processes reducing at different potentials IL

E E E ½ ½ Linear Scan Voltammetry (stirred) • Normally use Pt or C (graphite) electrodes • Better to use rotating electrode than stir bar • LSV can be used for quantitative analysis • Can measure many metal ions & organics • Fairly sensitive due to convective mass

transport, i.e., IF is large • The output signal in the form of a wave is considered a drawback – can be difficult to perform data analysis – multiple components gives stacked waves Linear Scan Voltammetry (stirred)

IL For a two component system it is difficult to measure the second species in the presence of a The second large concentration I becomes of the first species I L I L small since the range is set by the first species

E This problem is inherent for techniques that produce waves